The measurement of turbidity is useful in assessing samples in a variety of industries. Samples of specimens such as water, foods, fruit juices, and oils can be assessed based on turbidity, and a variety of processes in the brewing, petroleum, pulp and paper and chemical manufacturing industries can be assessed and controlled using turbidity measurements. Turbid samples present several measurement challenges, especially turbid samples having high optical attenuation. Measurement of the very large values of attenuation involved in turbidity measurement is difficult so that differences between highly scattering samples can be hard to quantify. In addition, typical samples can both absorb and scatter an incident measurement beam so that specimen absorption can produce errors in turbidity measurement. Although a wide range of instruments is available for turbidity measurement, alternative measurement approaches are needed, especially for high turbidities.